The Securities and Exchange Commission is drawing up plans to increase the number of people allowed to buy stakes in hot Silicon Valley startups and other private companies. But that population has already grown 10-fold since the 1980s, a Wall Street Journal analysis found.

More than 16 million U.S. households—about one in eight—are already allowed to invest directly in private companies, according to the analysis. Private companies don’t have to make the disclosures that public companies do, and regulators thus limit them...